Skip to main content
MathOverflow

Return to Answer

Added a reference + Math Jaxed
Source Link
Daniele Tampieri
Daniele Tampieri
  • 6.4k
  • 7
  • 30
  • 45

The sheaf cohomology Hi(X,F)${H}^i(X,F)$ of a (topological) manifold X$X$ of dimension n$n$ vanishes for i > n$i > n$. This is a topological version of Grothendieck's vanishing theorem above. You can find this result in Kashiwara-Schapira's "Sheaves on manifolds" proposition III.3.2.2.

Reference

Masaki Kashiwara, Pierre Schapira, [Houzel, Christian] Sheaves on manifolds. With a short history “Les débuts de la théorie des faisceaux” by Christian Houzel. (English) Grundlehren der Mathematischen Wissenschaften, 292. Berlin etc.: Springer-Verlag, pp. x+512 (1990), MR1074006, Zbl 0709.18001.

The sheaf cohomology Hi(X,F) of a (topological) manifold X of dimension n vanishes for i > n. This is a topological version of Grothendieck's vanishing theorem above. You can find this result in Kashiwara-Schapira's "Sheaves on manifolds" proposition III.3.2.2.

The sheaf cohomology ${H}^i(X,F)$ of a (topological) manifold $X$ of dimension $n$ vanishes for $i > n$. This is a topological version of Grothendieck's vanishing theorem above. You can find this result in Kashiwara-Schapira's "Sheaves on manifolds" proposition III.3.2.2.

Reference

Masaki Kashiwara, Pierre Schapira, [Houzel, Christian] Sheaves on manifolds. With a short history “Les débuts de la théorie des faisceaux” by Christian Houzel. (English) Grundlehren der Mathematischen Wissenschaften, 292. Berlin etc.: Springer-Verlag, pp. x+512 (1990), MR1074006, Zbl 0709.18001.

Source Link
Abdó Roig-Maranges
Abdó Roig-Maranges
  • 741
  • 4
  • 9

The sheaf cohomology Hi(X,F) of a (topological) manifold X of dimension n vanishes for i > n. This is a topological version of Grothendieck's vanishing theorem above. You can find this result in Kashiwara-Schapira's "Sheaves on manifolds" proposition III.3.2.2.